ViSOM － A Novel Method for Multivariate Data Projection and Structure Visualization Advisor : Dr. Hsu Graduate : Sheng-Hsuan Wang Author : Hujun Yin

Outline Motivation Objective Introduction Data Projection Methods ViSOM Experimental Results Conclusion Personal opinion Review

Motivation In SOM, the structures of the data clusters may not be apparent and their shapes are often distorted.

Objective In this paper, a visualization-induced SOM(ViSOM) is proposed to overcome these shortcomings.

Introduction The linear principal component analysis(PCA) － dimension reduction. Sammon mapping － nonlinear, minimize. Neural networks － can learn complex nonlinear relationships of variables. Ex:Self-Organization Maps(SOMs)

Introduction When the SOM is used for visualization, the inter-neuron distances are not directly visible or measurable on the map. － using a coloring scheme such as U-matrix.

Introduction The ViSOM projects as does the SOM, but constrains the lateral contraction force and regularizes the inter-neuron distance to a parameter that defines and controls the resolution of the map.

Data Projection Methods PCA PCA is a classic linear data analysis method aiming at finding orthogonal principal directions from a set of data, along which the data exhibit the largest variances.

Data Projection Methods Sammon Mapping A traditional subject related to dimension reduction and data projection is multidimensional scaling(MDS). A general fitness function, stress

Data Projection Methods Sammon Mapping The Sammon's mapping maps data points to the output space by minimizing the distance difference between data points in the input and output spaces.

Data Projection Methods SOM The SOM is an unsupervised learning algorithm that uses a finite grid of neurons to map or frame the input space.

ViSOM ViSOM Structure and Derivation The ViSOM uses a similar grid structure of neurons as does the SOM. A winning neuron v can be found according to its distance to the input, i.e.,

ViSOM Then the SOM updates the weight of the winning neuron according to The weight of the neurons in a neighborhood of the winner are updated by

ViSOM Decomposition of the SOM updating force

ViSOM ViSOM Algorithm Find the winner from (5). Update the winner according to (6). Update the neighborhood according to Refresh the map by randomly choosing the weights of the neurons.(optional)

ViSOM The rigidity of the map is controlled by the ultimate size,, of the neighborhood. The resolution parameter depends on the size of the map, data variance and required resolution of the map.

Experimental Results Two Illustrative Data Sets

Experimental Results

Iris Data Set

Conclusion In this paper, a new mapping method, ViSOM, is proposed for visualization and projection of high-dimensional data.

Personal Opinion This method can be used in our lab ’ s SOM program to improve the quality of clustering.

Review Data Projection Methods PCA Sammon Mapping SOM ViSOM